Unit 2: Periodicity of Elements

The Periodic Table

The Long Form of the Periodic Table (or Modern Periodic Table) organizes elements based on increasing atomic number (Z). Its structure is based on the electronic configuration of the atoms.

• Periods: The 7 horizontal rows are called periods. The period number corresponds to the principal quantum number (n) of the outermost shell.
• Groups: The 18 vertical columns are called groups. Elements in the same group have similar valence shell electronic configurations and thus similar chemical properties.

s-, p-, d-, f- block elements

Elements are classified into four blocks based on the subshell in which the last electron (or differentiating electron) enters.

Blocks of the Periodic Table

Block	Groups	Differentiating Electron Enters	Key Characteristics
s-block	1 (Alkali Metals) 2 (Alkaline Earth Metals)	ns subshell	Highly reactive metals, low ionization enthalpies.
p-block	13 to 18	np subshell	Includes metals, metalloids, and non-metals.
d-block	3 to 12	(n-1)d subshell	"Transition Metals." Form colored ions, show variable oxidation states.
f-block	(Inner-Transition)	(n-2)f subshell	"Inner-Transition Metals." Includes Lanthanides (4f) and Actinides (5f).

Effective Nuclear Charge and Slater's Rules

(a) Effective Nuclear Charge (Z_eff)

In a multi-electron atom, an electron is simultaneously attracted by the nucleus and repelled by the other electrons (inner-shell and valence-shell).

• Shielding or Screening Effect: The inner-shell electrons "shield" the outermost electron from the full pull of the nucleus. This repulsion from inner electrons effectively reduces the nuclear charge felt by the valence electron.

Definition (Effective Nuclear Charge, Z_eff): The net positive charge experienced by an electron in an atom.
Formula: Z_eff = Z - σ
Where: Z = Actual nuclear charge (Atomic Number), σ = Shielding constant (or Screening constant)

Slater's Rules (for calculating σ)

Slater provided a set of empirical rules to calculate the shielding constant (σ) for any electron.

1. Write the configuration: Group the electronic configuration as follows:
   (1s) (2s, 2p) (3s, 3p) (3d) (4s, 4p) (4d) (4f) ...
2. Identify the electron: We are calculating σ for a specific electron (e.g., a 3p electron).
3. Sum the contributions:
   • Electrons in groups outside (to the right of) the electron of interest contribute 0.
   • For an electron in an ns or np orbital:
     • Other electrons in the same (ns, np) group contribute 0.35 each.
     • Electrons in the (n-1) shell contribute 0.85 each.
     • Electrons in the (n-2) or deeper shells contribute 1.00 each.
   • For an electron in an nd or nf orbital:
     • Other electrons in the same (nd) or (nf) group contribute 0.35 each.
     • Electrons in all groups to the left (including s, p electrons of the same n) contribute 1.00 each.

Example: Calculate Z_eff for a 3p electron in Chlorine (Cl, Z=17)

Config: (1s²) (2s², 2p⁶) (3s², 3p⁵)

1. We are calculating σ for one of the 3p electrons.
2. Same group (3s, 3p): There are (2+5-1) = 6 other electrons.
   Contribution = 6 × 0.35 = 2.10
3. (n-1) shell (2s, 2p): There are 8 electrons.
   Contribution = 8 × 0.85 = 6.80
4. (n-2) shell (1s): There are 2 electrons.
   Contribution = 2 × 1.00 = 2.00
5. Total σ = 2.10 + 6.80 + 2.00 = 10.90
6. Z_eff = Z - σ = 17 - 10.90 = 6.10

Variation of Effective Nuclear Charge in Periodic Table

• Across a Period (Left to Right): Z_eff increases.
  Reason: The nuclear charge (Z) increases by +1, but the new electron is added to the same shell, so it only shields by 0.35. The net effect is a stronger pull (Z_eff increases).
• Down a Group (Top to Bottom): Z_eff increases slightly (or is relatively constant).
  Reason: While Z increases significantly, the (n-1) and deeper shells become very large, leading to almost complete shielding of the added nuclear charge. The Z_eff felt by the outermost electron changes very little down a group.

(b) Atomic Radii (van der Waals)

The "size" of an atom is hard to define because the electron cloud has no sharp boundary. We define atomic radii based on how close atoms get to each other in different situations.

Types of Atomic Radii (for context):

• Covalent Radius: Half the distance between the nuclei of two identical atoms joined by a single covalent bond.
• Metallic Radius: Half the distance between the nuclei of two adjacent metal atoms in a metallic crystal.

van der Waals Radius

Definition: Half the internuclear distance between two identical, non-bonded, adjacent atoms in their solid state (e.g., in a crystal of a noble gas, or between two different molecules).

This radius measures the distance of closest approach for two non-bonded atoms.
Key Point: van der Waals radius > Covalent radius (e.g., for Cl, covalent radius is 99 pm, vdW radius is 180 pm).

This radius is used for noble gases (which don't form bonds) and to determine the "packing" of molecules in solids.

Periodic Trends in Atomic Radii

• Across a Period (Left to Right): Atomic radii decrease.
  Reason: Z_eff increases, pulling the electron shells closer to the nucleus.
• Down a Group (Top to Bottom): Atomic radii increase.
  Reason: A new principal energy level (n) is added, which is much farther from the nucleus. This "new shell" effect is much stronger than the slight increase in Z_eff.

(c) Ionization Enthalpy (IE)

Definition (First Ionization Enthalpy, IE₁): The minimum energy required to remove the most loosely bound electron from an isolated, gaseous atom in its ground state.
X(g) + Energy → X⁺(g) + e^-

Successive Ionization Enthalpies

These refer to the removal of subsequent electrons (2nd, 3rd, etc.).

• X⁺(g) → X²⁺(g) + e^- (Second IE, IE₂)
• X²⁺(g) → X³⁺(g) + e^- (Third IE, IE₃)

Key Point: IE₁ < IE₂ < IE₃ < ...
Reason: It is always harder to remove an electron from a positive ion (cation) than from a neutral atom because the Z_eff is higher (fewer electrons to repel each other).
A very large jump in IE occurs when an electron is removed from a stable, filled inner shell (a noble gas core).

Factors Affecting Ionization Enthalpy

1. Effective Nuclear Charge (Z_eff): Higher Z_eff → Stronger attraction → Higher IE.
2. Atomic Size: Larger atomic radius → Electron is farther from nucleus → Weaker attraction → Lower IE.
3. Penetration Effect: For the same shell (n), an s-electron penetrates closer to the nucleus than a p-electron.
   Penetration: s > p > d > f.
   Therefore, for the same n, IE(s) > IE(p) > IE(d) > IE(f).
4. Stability of Half-filled / Full-filled Subshells: These configurations are extra stable.
   Example: IE₁ of Nitrogen (p³, half-filled) > IE₁ of Oxygen (p⁴).
   Example: IE₁ of Be (s², full-filled) > IE₁ of Boron (p¹).

Applications of Ionization Enthalpy

• Metallic Character: Low IE → Easy to remove electron → High metallic character.
• Reactivity: Low IE (like Alkali Metals) → Very reactive. High IE (like Noble Gases) → Inert.
• Stable Oxidation States: A large jump in successive IEs indicates a stable oxidation state.
  Example: For Mg, IE₁ = 737, IE₂ = 1450, but IE₃ = 7730 kJ/mol. The huge jump at IE₃ shows that Mg will readily form Mg²⁺ but not Mg³⁺.

(d) Electron Gain Enthalpy (Δ H_eg)

Definition: The enthalpy change (Δ H) that occurs when an electron is added to an isolated, gaseous atom in its ground state.
X(g) + e^- → X^-(g)

• If Δ H_eg is negative, energy is released (exothermic). This means the atom "wants" the electron (high electron affinity).
• If Δ H_eg is positive, energy is absorbed (endothermic). This means the atom "does not want" the electron (e.g., Noble Gases, N, Be).

Trends of Electron Gain Enthalpy

• Across a Period (Left to Right): Δ H_eg generally becomes more negative.
  Reason: Z_eff increases, so the nucleus attracts the incoming electron more strongly. Halogens (Group 17) have the most negative Δ H_eg.
• Down a Group (Top to Bottom): Δ H_eg generally becomes less negative (more positive).
  Reason: The new electron is added to a shell farther from the nucleus, so it is less strongly attracted.

Key Exceptions:

• Noble Gases (Group 18): Have positive Δ H_eg. The new electron must enter the next (higher n) shell, which is highly unfavorable.
• N and Be: Have near-zero or positive Δ H_eg due to stable half-filled (N, p³) and full-filled (Be, s²) subshells.
• Fluorine vs. Chlorine (CRUCIAL): We expect F > Cl (i.e., F to be more negative).
  Actual Trend: Δ H_eg of Chlorine is more negative than Fluorine.
  Reason: Fluorine is very small. The incoming electron faces strong inter-electronic repulsion from the 9 electrons already crowded in the small 2p subshell. Chlorine (in n=3) has more space, so repulsion is less.
  Order: Cl > F > Br > I

(e) Electronegativity (χ)

Definition: The relative tendency of an atom, when it is in a chemical bond, to attract the shared pair of electrons towards itself.

This is a relative property (a unitless number on a scale), not a measurable energy value like IE or EGE.

Electronegativity Scales

1. Pauling's Scale

This is the most common scale. It is based on bond energies. Pauling reasoned that the A-B bond energy is stronger than the average of A-A and B-B bonds due to an "ionic resonance" contribution, which depends on the EN difference.

Formula: χ_A - χ_B = 0.208 √(Δ) (when energies are in kcal/mol)
Where Δ = E_A-B - √(E_A-A · E_B-B)

He arbitrarily set χ_F = 4.0 (most electronegative) and calculated others relative to it.

2. Mulliken's Scale

Mulliken defined EN as the simple average of an atom's Ionization Enthalpy (tendency to lose e-) and its Electron Affinity (tendency to gain e-).

Formula: χ_M = (IE + EA) / (2)

This scale gives larger numbers, but they are proportional to Pauling's scale: χ_P ≈ (χ_M) / (2.8) (if IE and EA are in eV).

3. Allred-Rochow's Scale

This scale defines EN as the electrostatic force exerted by the Z_eff on the valence electrons at the covalent radius (r_cov).

Formula: χ_AR = ( 0.359 × (Z_eff) / (r_cov²) ) + 0.744
(where r_cov is in Angstroms, \AA)

Periodic Trends in Electronegativity

• Across a Period (Left to Right): EN increases.
  Reason: Z_eff increases and atomic radius decreases.
• Down a Group (Top to Bottom): EN decreases.
  Reason: Atomic radius increases, so the shared electrons are farther from the nucleus.